The overall aim of this project is to use state-of-the-art high field (3T) functional magnetic resonance imaging (fMRI) to identify and assess the neural circuits involved in various types of mathematical processing in third grade children studied in Project 1 (Cognition, and to evaluate quantitatively the effects on brain function of specific interventions developed in Project 2 (Intervention). These studies would be performed in well characterized groups of third graders with difficulties only in math (MD), both math and reading (MD-RD), only reading difficulties (RD), and normal controls. In addition, we will use high resolution MR imaging to measure morphological differences, and diffusion tensor imaging to assess structural differences in white matter tracts, among these groups. Previous fMRI studies in adults have demonstrated that different types of mathematical processing engage specific neural regions. The intraparietal area bilaterally has been found to activate in number processing and it has been proposed that this region encodes numerical quantity in a non-verbal semantic fashion. Retrieval of this representation of quantity becomes automatic with normal development. In addition, intraparietal cortex is activated for approximation tasks in which estimates are based on distances between different quantities. It is hypothesized that different mathematical abilities will show different recruitment patterns of these various areas, and that specific disabilities will manifest themselves as abnormal patterns of activation. Based on studies with other types of disabilities, we expect the activation within these regions will correlate with mathematical skill and will therefore show changes with positive effects of interventions. These hypotheses will be tested by imaging children with both normal and impaired mathematical skills, with and without associated reading problems. We will quantitatively describe the patterns of brain activation associated with different levels of performance in exact calculation (fact retrieval) tasks and estimation tasks, in children with mathematical disability (MD), reading disability (RD), co-occurring MD-RD, and normal controls, and correlate fMRI data with behavioral data collected in Project 1 (Cognition). We will also quantitatively evaluate regional changes in brain activation following each of two different types of intervention: treatments that systematically vary fact retrieval and procedural skill instruction, and treatments that systematically vary arithmetic word problem instruction with and without fact retrieval instruction. Our overall aims are to use modern imaging tools to identify the recruitment patterns within the brain that correlate with mathematical ability, especially in the absence of other (reading) disabilities; to assess whether differences can be found in these neural substrates between different groups (identified by learning and skill in mathematics and reading); and to quantify the effects of different interventions.